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Array of Equilateral Triangles

Array of Equilateral Triangles
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2014-07-26 00:11
TriangleVector
Demonstrates symmetry in an array of equilateral triangles; involves concepts of equilateral triangles, vectors, and transformations; constructed using commands like Polygon, Translate, and Rotate; suitable for high school geometry education.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Point(a) → D
  3. Vector(C, D) → u
  4. Translate(poly1, u) → poly1'
  5. Rotate(u, 60*°, C) → v
  6. Translate(poly1, v) → poly1'_1
  7. Sequence(Translate[Sequence[Translate[poly1, Vector[(n * u)]], n, -10, 10], Vector[(m * v)]], m, -10, 10) → list1
  8. Translate(A, w) → A'
  9. Translate(B, Vector[(-v)]) → B'
  10. Polygon(D, A', B') → poly2, b', d, a'
  11. Sequence(Translate[Sequence[Polygon[Translate[D, Vector[(n * u)]], Translate[A', Vector[(n * u)]], Translate[B', Vector[(n * u)]]], n, -10, 10], Vector[(m * v)]], m, -10, 10) → list2

AI Drawing Prompt Reference

Draw an array of equilateral triangles to demonstrate symmetry. Start with a single equilateral triangle, then use vector translation and rotation to create multiple copies, forming a symmetric pattern. Apply repeated translations and rotations based on vectors to generate a complex grid of triangles, highlighting symmetry and transformation relationships.
The prompt above was compiled from the original drawing commands and is for reference only.